Describing ONE Variable What is the typical value? Central Tendency Measures Mode Median Mean How Typical is the typical value? Measures of Variation Range InterQuartile Range IQR Variance/Standard Deviation

Central Tendency Measures What is the typical value? Mode most frequent value Median –50 th percentile Mean (Average) ΣX i /N

Which central tendency measure to use when? ModeMedianMean NominalYesNo OrdinalYes No Interval and Ratio Yes

Measures of Variability How typical is the typical value? Range – Maximum-Minimum Interquartile Range –Difference between the 25 th and 75 th percentile Variance –Average Squared Deviation from the Mean Σ[Xi-Mean(Xi)] 2 /N Corrected variance Σ[Xi-Mean(Xi)] 2 /(N-1)

Which variability measure to use when? RangeInterquartile Range Variance/ Stand.Dev. NominalNo OrdinalYes No Interval/ Ratio Yes

Describing Relationships Between TWO Variables Tables Independent Variable Column/Dependent Variable Row Percentage Difference For dichotomies difference of two column percentages in the same row Cramer’s V For nominal variables Gamma For ordinal variables

Describing Associations Strength –Percentage difference |50%-60%|=10%

Observed vs. Expected Tables MENWOMENTOTALMENWOMENTOTAL DEM100 (50%) 120 (60%) 220 (55%) 110 (55%) 110 (55%) 220 REPUBL ICAN 100 (50%) 80 (40%) 180 (45%) 90 (45%) 90 (45%) 180 TOTAL

Chi -Square ( ) 2 /110+( ) 2 /110+ (100-90) 2 /90 +(80-90) 2 /90= 100/ / /90+100/90= = 4.04 SUM[Fo ij -Fe ij ] 2 /Fe ij =Chi-Square

Cramer’s V Cramer’s V=SQRT[Chi-Square/(N*Min(c-1,r-1)] Cramer’s V is between 0 (no relationship) and 1 (perfect relationship) V=SQRT[4.04/400*1]=.1005

Evaluating Relationships Existence Strength, Direction Pattern Statistical Significance: –Can we generalize from our sample to the population? –The values show the probability of making a mistake if we did. More precisely: The probability of getting a relationship this strong or stronger from a population where that relationship does not exist, just by sampling error.